New Results on Majorized Discrete Jensen–Mercer Inequality for Raina Fractional Operators

English (OpenAlex)

As the most important inequality, the Hermite–Hadamard–Mercer inequality has attracted the interest of numerous additional mathematicians. Numerous findings on this inequality have been developed in recent years. So, in this paper, we demonstrate novel Hermite–Hadamard–Mercer inequalities using Raina fractional operators and the majorization concept. Furthermore, additional identities are discovered, and two new lemmas of this type are proved. A summary of several known results is also provided, along with a thorough derivation of some exceptional cases. We also note that some of the outcomes in this study are more acceptable than others under certain exceptional instances, such as setting n=2, w=0, σ(0)=1, and λ=1 or λ=α. Lastly, the method described in this publication is thought to stimulate further research in this area.